LCM of 10 and 15 is 30. The LCM of any two numbers is the number evenly divisible by the two given numbers. The least common multiple of 10 and 15 is the value we get from the common multiples. (10, 20, 30, 40, 50, 60, 70, ….) and (15, 30, 45, 60, 75, 90,….) are the multiples of 10 and 15. We can find the LCM of two numbers using methods such as prime factorisation, division and listing the multiples.
Also read: Least common multiple
What is LCM of 10 and 15?
The answer to this question is 30. The LCM of 10 and 15 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 10 and 15, is the smallest positive integer 30 which is divisible by both 10 and 15 with no remainder.
How to Find LCM of 10 and 15?
LCM of 10 and 15 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 10 and 15 Using Prime Factorisation Method
The prime factorisation of 10 and 15, respectively, is given by:
10 = 2 x 5 = 2¹ x 5¹
15 = 3 x 5 = 3¹ x 5¹
LCM (10, 15) = 30
LCM of 10 and 15 Using Division Method
We’ll divide the numbers (10, 15) by their prime factors to get the LCM of 10 and 15 using the division method (preferably common). The LCM of 10 and 15 is calculated by multiplying these divisors.
| 2 | 10 | 15 |
| 3 | 5 | 15 |
| 5 | 5 | 5 |
| 1 | 1 |
No further division can be done.
Hence, LCM (10, 15) = 30
LCM of 10 and 15 Using Listing the Multiples
To calculate the LCM of 10 and 15 by listing out the common multiples, list the multiples as shown below.
| Multiples of 10 | Multiples of 15 |
| 10 | 15 |
| 20 | 30 |
| 30 | 45 |
| 40 | 60 |
| 50 | 75 |
LCM (10, 15) = 30
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Video Lesson on Applications of LCM
LCM of 10 and 15 Solved Examples
Question: Determine the smallest number that is divisible by 10 and 15.
Solution:
We know that
The smallest number which is exactly divisible by 10 and 15 is the LCM.
Multiples of 10 = 10, 20, 30, 40, 50, 60, 70, …..
Multiples of 15 = 15, 30, 45, 60, 75, 90, 105, ….
Hence, the LCM of 10 and 15 is 30.
Frequently Asked Questions on LCM of 10 and 15
Find the LCM of 10 and 15 using the prime factorization method.
To determine the LCM using the prime factorization, we first have to find the prime factors.
10 = 2 x 5
15 = 3 x 5
LCM of 10 and 15 is the product of prime factors raised to the highest exponent among the numbers 10 and 15
LCM of 10 and 15 = 2¹ x 3¹ x 5¹ = 30
What is the GCF if the LCM of 10 and 15 is 30?
LCM x GCF = 10 x 15
Given
LCM of 10 and 15 = 30
30 x GCF = 150
GCF = 150/30 = 5
Write the relation between GCF and LCM of 10 and 15.
The relation between GCF and LCM of 10 and 15 is
LCM x GCF = 10 x 15
LCM x GCF = 150
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